A. Field
The present disclosure pertains generally to lasers and more particularly to ultrafast mode-locked pulsed lasers. In one aspect this disclosure discusses carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis
B. Background
1. Introduction. Progress in femtosecond pulse generation has made it possible to generate optical pulses that are only a few cycles in duration. [See G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, U. Keller, Science 286,1507 (1999); M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. C. Kapteyn, M. M. Murnane, Opt. Lett. 18, 977 (1993); U. Morgner, F. X. Kartner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, T. Tschudi, Opt. Lett. 24, 411 (1999); D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller, V. Scheuer, G. Angelow, T. Tschudi, Opt. Left. 24, 631 (1999)]. This has resulted in rapidly growing interest in controlling the phase of the underlying carrier wave with respect to the envelope. [See G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, U. Keller, Science 286,1507 (1999); L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, T. W. Hansch, Opt. Lett. 21, 2008 (1996); P. Dietrich, F. Krausz, P. B. Corkum, Opt. Lett. 25, 16 (2000); R. J. Jones, J.-C. Diels, J. Jasapara, W. Rudolph, Opt. Commun. 175,409 (2000)]. The “absolute” carrier phase is normally not important in optics; however, for such ultrashort pulses, it can have physical consequences. [See P. Dietrich, F. Krausz, P. B. Corkum, Opt. Lett. 25, 16 (2000); C. G. Durfee, A. Rundquist, S. Backus, C. Heme, M. M. Murname, H. C. Kapteyn, Phys. Rev. Lett. 83, 2187 (1999)]. Concurrently, mode-locked lasers, which generate a train of ultrashort pulses, have become an important tool in precision optical frequency measurement. [See T. Udem, J. Reichert, R. Holzwarth, T. W. Hänsch, Phys. Rev. Lett. 82, 3568 (1999); T. Udem, J. Reichert, R. Holzwarth, T. W. Hänsch, Opt. Lett. 24, 881 (1999); J. Reichert, R. Holzwarth, Th. Udem, T. W. Hänsch, Opt. Comm. 172, 59 (1999); S. A. Diddams, D. J. Jones, L.-S. Ma, S. T. Cundiff, J. L. Hall, Opt. Lett. 25, 186 (2000); S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, T. W. Häsch, Phys. Rev. Lett. 84, 5102 (2000); Various schemes for using mode-locked lasers in optical frequency metrology were recently discussed in H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, U. Keller, Appl. Phys. B 69, 327 (1999)]. There is a close connection between these two apparently disparate topics. This connection has been exploited in accordance with the present invention to develop a frequency domain technique that stabilizes the carrier phase with respect to the pulse envelope. Using the same technique, absolute optical frequency measurements were performed in accordance with the present invention using a single mode-locked laser with the only input being a stable microwave clock.
Mode-locked lasers generate a repetitive train of ultrashort optical pulses by fixing the relative phases of all of the lasing longitudinal modes. [See A. E. Siegman, Lasers, (University Science Books, Mill Valley Calif., 1986), p. 1041-1128]. Current mode-locking techniques are effective over such a large bandwidth that the resulting pulses can have a duration of 6 femtoseconds or shorter, i.e., approximately two optical cycles. [See M. T. Asaki, C.-P. Huang, D. Garvey, J. Zhou, H. C. Kapteyn, M. M. Murnane, Opt. Lett. 18, 977 (1993); U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Schenuer, G. Angelow, T. Tschudi, Opt. Lett. 24, 411 (1999); D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. Morier-Genoud, U. Keller V. Scheuer, G. Angelow, T. Tschudi, Opt. Lett. 24, 631 (1999)]. With such ultrashort pulses, the relative phase between the peak of the pulse envelope and the underlying electric-field carrier wave becomes relevant. In general, this phase is not constant from pulse-to-pulse because the group and phase velocities differ inside the laser cavity (see FIG. 7A). To date, techniques of phase control of femtosecond pulses have employed time domain methods. [See L. Xu, Ch. Spielmann, A. Poppe, T. Brabec, F. Krausz, T. W. Hänsch, Opt. Lett. 21, 2008 (1996)]. However, these techniques have not utilized active feedback, and rapid dephasing occurs because of pulse energy fluctuations and other perturbations inside the cavity. Active control of the relative carrier-envelope phase prepares a stable pulse-to-pulse phase relationship, as presented below, and will dramatically impact extreme nonlinear optics.
At the present, measurement of frequencies into the microwave regime (tens of gigahertz) is straightforward thanks to the availability of high frequency counters and synthesizers. Historically, this has not always been the case, with direct measurement being restricted to low frequencies. The current capability arose because an array of techniques was developed to make measurement of higher frequencies possible. [See G. E. Sterling and R. B. Monroe, The Radio Manual (Van Nostrand, New York, 1950)]. These techniques typically rely on heterodyning to produce an easily measured frequency difference (zero-beating being the limit). The difficulty lay in producing an accurately known frequency to beat an unknown frequency against.
Measurement of optical frequencies (hundreds of terahertz) has been in a similar primitive state until recently. This is because only few “known” frequencies have been available and it has been difficult to bridge the gap between a known frequency and an arbitrary unknown frequency of the gap exceeds tens of gigahertz (about 0.01% of the optical frequency). Furthermore, establishing known optical frequencies was itself difficult because an absolute measurement of frequency must be based on the time unit “second”, which is defined in terms of the microwave frequency of a hyperfine transition of the cesium atom. This requires a complex “clockwork” to connect optical frequencies to those in the microwave region.
Optical frequencies have been used in measurement science since shortly after the invention of lasers. Comparison of a laser's frequency of ˜5×1014 Hz with its ideal˜milliHertz linewidth, produced by the fundamental phase diffusion of spontaneous emission, reveals a potential dynamic range of 1017 in resolution, offering one of the best tools for discovering new physics in “the next decimal place”. Nearly forty years of vigorous research in the many diverse aspects of this field by a worldwide community have resulted in exciting discoveries in fundamental science and development of enabling technologies. Some of the ambitious long-term goals in optical frequency metrology are just coming to fruition owing to a number of recent spectacular technological advances, most notably, the use of mode-locked lasers for optical frequency synthesis. Other examples include laser frequency stabilization to one Hz and below [B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799-3802 (1999)], optical transitions observed at a few Hz linewidth (corresponding to a Q of 1.5×1014) [R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462-2465 (2000)] and steadily improving accuracy of optical standards with a potential target of 10−18 for cold atom/ion systems.
2. Optical Frequency Synthesis and Metrology. Optical frequency metrology broadly contributes to and profits from many areas in science and technology. At the core of this subject is the controlled and stable generation of coherent optical waves, i.e. optical frequency synthesis. This permits high precision and high resolution measurement of many physical quantities.
Below brief discussions are provided on these aspects of optical frequency metrology, with stable lasers and wide bandwidth optical frequency combs making up the two essential components in stable frequency generation and measurement.
a. Establishment of standards. In 1967, just a few years after the invention of the laser, the international standard of time/frequency was established, based on the F=4, mF=0 F=3, mF=0 transition in the hyperfine structure of the ground state of 133Cs. [See N. F. Ramsey, Journal of Res. of NBS 88, 301-320 (1983)]. The transition frequency is defined to be 9,192,631,770 Hz. The resonance Q of ˜108 is set by the limited coherent interaction time between matter and field. Much effort has been invested in extending the coherent atom-field interaction time and in controlling the first and second order Doppler shifts. Recent advances in the laser cooling and trapping technology have led to the practical use of laser-slowed atoms, and a hundred-fold resolution enhancement. With the reduced velocities, Doppler effects have also been greatly reduced. Cs clocks based on atomic fountains are now operational with reported accuracy of 3×10−15 and short term stability of 1×10−13 at 1 second, limited by the frequency noise of the local rf crystal oscillator. [See C. Santarelli, P. Laurent, P. Lemonde, A. Clairon, A. G. Mann, S. Chang, A. N. Luiten, and C. Salomon, Phys. Rev. Lett. 82, 4619-4622 (1999)]. Through similar technologies, single ions, laser-cooled and trapped in an electromagnetic field, are now also excellent candidates for radio frequency/microwave standards with a demonstrated frequency stability approaching 3×10−13 at 1 second. [See Sullivan, D. B., J. C. Bergquist, J. J. Bollinger, R. E. Drullinger, W. M. Itano, S. R. Jefferts, W. D. Lee, D. Meekhof, T. E. Parker, F. L. Walls, D. J. Wineland, “Primary Atomic Frequency Standards at NIST”, J. Res. NIST, 2001, 106(1) pp47-63; D. J. Berkeland, J. D. Miller, J. C. Berquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 80, 2089-2092 (1998)]. More compact, less expensive, (and less accurate) atomic clocks use cesium or rubidium atoms in a glass cell, equipped with all essential clock mechanisms, including optical pumping (atom preparation), microwave circuitry for exciting the clock transition, and optical detection. The atomic hydrogen maser is another mature and practical device that uses the radiation emitted by atoms directly. [See H. M. Goldenberg, D. Kleppner, and N. F. Ramsey, Phys. Rev. Lett. 8, 361 (1960)]. Although it is less accurate than the cesium standard, a hydrogen maser can realize exceptional short-term stability.
The development of optical frequency standards has been an extremely active field since the invention of lasers, which provide the coherent radiation necessary for precision spectroscopy. The coherent interaction time, the determining factor of the spectral resolution in many cases, is in fact comparable in both optical and rf domains. The optical part of the electromagnetic spectrum provides higher operating frequencies. Therefore the quality factor, Q, of an optical clock transition is expected to be a few orders higher than that available in the microwave domain. A superior Q factor helps to improve all three essential characteristics of a frequency standard, namely accuracy, reproducibility and stability. Accuracy refers to the objective property of a standard to identify the frequency of a natural quantum transition, idealized to the case that the atoms or the molecules are at rest and free of any perturbation. Reproducibility measures the repeatability of a frequency standard for different realizations, signifying adequate modeling of observed operating parameters and independence from uncontrolled operating conditions. Stability indicates the degree to which the frequency stays constant after operation has started. Ideally, a stabilized laser can achieve a fractional frequency stability                     δ        ⁢                                   ⁢        v            v        =                  1        Q            ⁢              1                  S          /          N                    ⁢              1                  τ                      ,where S/N is the recovered signal-to-noise ratio of the resonance information, and τ is the averaging time. Clearly it is desirable to enhance both the resolution and sensitivity of the detected resonance, as these control the time scale necessary for a given measurement precision. The reward is enormous: enhancing the Q (or S/N) by a factor of ten reduces the averaging time by a factor of 100.
The nonlinear nature of a quantum absorption process, while limiting the attainable S/N, permits sub-Doppler resolution. Special optical techniques invented in the 70's and 80's for sub-Doppler resolution include saturated absorption spectroscopy, two-photon spectroscopy, optical Ramsey fringes, optical double resonance, quantum beats and laser cooling and trapping. Cold samples offer the true possibility to observe the rest frame atomic frequency. Sensitive detection techniques, such as polarization spectroscopy, electron shelving (quantum jump), and frequency modulation optical heterodyne spectroscopy, were also invented during the same period, leading to an absorption sensitivity of 1×10−8 and the ability to split a MHz scale linewidth typically by a factor of 104-105, at an averaging time of ˜1 s. All these technological advances paved the way for sub-Hertz stabilization of super-coherent optical local oscillators.
To effectively use a laser as a stable and accurate optical local oscillator, active frequency control is needed, owing to the strong coupling between the laser frequency and the laser parameters. The simultaneous use of quantum absorbers and an optical cavity offers an attractive laser stabilization system. A passive reference cavity brings the benefit of a linear response allowing use of sufficient power to achieve a high S/N. On one hand, a laser pre-stabilized by a cavity offers a long phase coherence time, reducing the need for frequent interrogations of the quantum absorber. In other words, the laser linewidth over a short time scale is narrower than the chose atomic transition width and thus the information of the natural resonance can be recovered with an optimal S/N and the long averaging time translates into a finer examination of the true line center. On the other hand, the quantum absorber's resonance basically eliminates inevitable drifts associated with material standards, such as a cavity. Frequency stability in the 10−16 domain has been measured with a cavity-stabilized laser. [See C. Salomon, D. Hils, and J. L. Hall, J. Opt. Soc. Am. B 5, 1576-1587 (1988)]. The use of frequency modulation for cavity/laser lock has become a standard laboratory practice. [See R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, App. Phys. B 31, 97-105 (1983)]. Tunability of such a cavity/laser system can be obtained by techniques such as the frequency-offset optical phase-locked-loop (PLL).
A broad spectrum of lasers have been stabilized, from early experiments with gas lasers (He—Ne, CO2, Ar+, etc.) to more recent tunable dye lasers, optically pumper solid-state lasers Ti:Sapphire, YAG, etc.) and diode lasers. Usually one or several atomic or molecular transitions are located within the tuning range of the laser to be stabilized. The use of molecular ro-vibrational lines for laser stabilization has been very successful in the infrared, using molecules such as CH4, CO2 and OsO4. [See T. J. Quinn, Metrologia 36, 211-244 (1999)]. Their natural linewidths range below a kilohertz, as limited by molecular fluorescent decay. Useable linewidths are usually 10 kHz due to transit of molecules through the light beam. Transitions to higher levels of these fundamental ro-vibrational states, usually termed overtone bands, extend these ro-vibrational spectra well into the visible with similar ˜kHz potential linewidths. Until recently, the rich spectra of the molecular overtone bands have not been adopted as suitable frequency references in the visible due to their small transition strengths. [See M. Delabachelerie, K. Nakagawa, and M. Ohstru, Opt. Lett. 19, 840-842 (1994)]. However, with one of the most sensitive absorption techniques, which combines frequency modulation with cavity enhancement, an excellent S/N for these weak but narrow overtone lines can be achieved [J. Ye, L. S. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6-15 (1998)], enabling the use of molecular overtones as standards in the visible. [See J. Ye, L. S. Ma, and J. L. Hall, IEEE Trans. Instrum. Meas. 46, 178-182 (1997); J. Ye, L. S. Ma, and J. L. Hall, J. Opt. Soc. Am. B 17, 927-931 (2000)].
Systems based on cold absorber samples potentially offer the highest quality optical frequency sources, mainly due to the drastic reductions of linewidth and velocity-related systematic errors. For example, a few Hz linewidth on the uv transition of Hg+ was recently observed at NIST. [See R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462-2465 (2000)]. Current activity on single ion systems includes Sr+ [J. E. Bernard, A. A. Madej, L. Marmet, B. G. Whitford, K. J. Siemsen, and S. Cundy, Phys. Rev. Lett. 82, 3228-3231 (1999)] Yb+ [M. Roberts, P. Taylor, G. P. Barwood, P. Gill, H. A. Klein, and W. R. C. Rowley, Phys. Rev. Lett. 78, 1876-1879 (1997)] and In+, [E. Peik, J. Abel, T. Becker, J. von Zanthier, and H. Walther, Phys. Rev. A 60, 439-449 (1999)]. One of the early NIST proposals of using atomic fountains for optical frequency standards [J. L. Hall, M. Zhu, and P. Buch, J. Opt. Soc. Am. B 6, 2194-2205 (1989)] has resulted in investigation of the neutral atoms Mg, Ca, Sr, Ba, and Ag. These systems could offer ultimate frequency standards free from virtually all of the conventional shifts and broadenings, to the level of one part in 1016-1018. Considerations of a practical system must always include its cost, size and degree of complexity. Compact and low cost systems can be competitive even though their performance may be 10-fold worse compared with the ultimate system. One such system is Nd:YAG laser stabilized on HCCD at 1064 nm or on I2 (after frequency doubling) at 532 nm, with a demonstrated stability level of 4×10−15 at 300-s averaging time. [See J. Ye, L. Robertsson, S. Picard, L. S. Ma, and J. L. Hall, IEEE Trans. Instrum. Meas. 48, 544-549 (1999); J. L. Hall, L. S. Ma, M. Taubman, B. Tiemann, F. L. Hong, O. Pfister, and J. Ye, IEEE Trans. Instrum. Meas. 48, 583-586 (1999)]. FIG. 1 summarizes some of the optical frequency standards 100 that are either established or under active development. Also indicated is the spectral width of currently available optical frequency combs 102 generated by mode-locked lasers.
Accurate knowledge of the center of the resonance is essential for establishing standards. Collisions, electromagnetic fringe fields, residual Doppler effects, probe field wave-front curvature, and probe power can all produce undesired center shifts and linewidth broadening. Other physical interactions, and even distortion in the modulation waveform, can produce asymmetry in the recovered signal line shape. For example, in frequency modulation spectroscopy, residual amplitude modulation introduces unwanted frequency shifts and instability and therefore needs to be controlled. [See J. L. Hall, J. Ye, L.-S. Ma, K. Vogel, and T. Dinneen, in Laser Spectroscopy XIII, edited by Z.-J. Wang, Z.-M. Zhang and Y.-Z. Wang (World Scientific, Sinagpore, 1998), p. 75-80]. These issues must be addressed carefully before one can be comfortable talking about accuracy. A more fundamental issue related to time dilation of the reference system (second order Doppler effect) can be solved in a controlled fashion, one simply knows the sample velocity accurately (for example, by velocity selective Raman process), or the velocity is brought down to a negligible level using cooling and trapping techniques.
b. Application of Standards. The technology of laser frequency stabilization has been refined and simplified over the years and has become an indispensable research tool in many modern laboratories involving optics. Research on laser stabilization has been and still is pushing the limits of measurement science. Indeed, a number of currently active research projects on fundamental physical principles greatly benefit from stable optical sources and need continued progress on laser stabilization. They include: laser test of fundamental principles [D. Hils and J. L. Hall, Phys. Rev. Lett. 64, 1697-1700 (1990)], gravitational wave detection [P. Fritschel, G. Gonzalez, B. Lantz, P. Saha, and M. Zucker, Phys. Rev. Lett. 80, 3181-3184 (1998)], quantum dynamics [H. Mabuchi, J. Ye, and H. J. Kimble, Appl. Phys. B 68, 1095-1108 (1999)], atomic and molecular structure, and many more. Recent experiments with hydrogen atoms have led to the best reported value for the Rydberg constant and 1S-Lamb shift. [See T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, Phys. Rev. Lett. 79, 2646-2649 (1997); C. Schwob, L. Jozefowski, B. deBeauvoir, L. Hilico, F. Nez, L. Julien, F. Biraben, O. Acef, and A. Clairon, Phys. Rev. Lett. 82, 4960-4963 (1999)]. Fundamental physical constants such as the fine-structure constant, ratio of Planck's constant to electron mass, and the electron-to-proton mass ratio are also being determined with increasing precision using improved precision laser tools. [See A. Peters, K. Y. Chung, B. Young. J. Hensley, and S. Chu, Philos. Trans. R. Soc. Lond. Ser. A 335, 2223-2233 (1997)]. Using extremely stable phase-coherent optical sources, we are entering an exciting era when picometer resolution can be achieved over a million kilometer distance in space. In time-keeping, an optical frequency clock is expected eventually to replace the current microwave atomic clocks. In length metrology, the realization of the basic unit, the “metre”, relies on stable optical frequencies. In communications, optical frequency metrology provides stable frequency/wavelength reference grids. [See T. Ikegami, S. Sudo, and Y. Sakai, Frequency stabilization of semiconductor laser diodes (Artech House, Norwood, 1995)].
A list of just a few examples of stabilized cw tunable lasers includes milliHertz linewidth stabilization (relative to a cavity) for diode-pumped solid state lasers, tens of milliHertz linewidth for Ti:Sapphire lasers and sub-Hertz linewidths for diode and dye lasers. Tight phase locking between different laser systems can be achieved [J. Ye and J. L. Hall, Opt. Lett. 24, 1838-1840 (1999)] even for diode lasers that have fast frequency noise.
c. Challenge of Opitical Frequency Measurement & Synthesis. Advances in optical frequency standards have resulted in the development of absolute and precise frequency measurement capability in the visible and near-infrared spectral regions. A frequency reference can be established only after it has been phase-coherently compared and linked with other standards. As mentioned above, until recently optical frequency metrology has been restricted to the limited set of “known” frequencies, due to the difficulty in bridging the gap between frequencies and the difficulty in establishing the “known” frequencies themselves.
The traditional frequency measurement takes a synthesis-by-harmonics approach. Such a synthesis chain is a complex system, involving several stages of stabilized transfer lasers, high-accuracy frequency references (in both optical and rf ranges), and nonlinear mixing elements. Phase-coherent optical frequency synthesis chains linked to the cesium primary standard include Cs—HeNe/CH4 (3.9 μm) [K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, Appl. Phys. Lett. 22, 192 (1973); C. O. Weiss, G. Kramer, B. Lipphardt, and E. Garcia, IEEE J. Quantum Electron. 24, 1970-1972 (1988)] and Cs—CO2/OsO4 (10 μm). [See A. Clairon, B. Dahmani, A. Filimon, and J. Rutman, IEEE Trans. Instrum. Meas. 34, 265-268 (1985)]. Extension to HeNe/I2 (576 nm) [C. R. Pollock, D. A. Jennings, F. R. Petersen, J. S. Wells, R. E. Drullinger, E. C. Beaty, and K. M. Evenson, Opt. Lett. 8, 133-135 (1983)] and HeNe/I2 (633 nm) [D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, and H. P. Layer, Opt. Lett. 8, 136-138 (1983); O. Acef, J. J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, P. Laurent, Y. Millerioux, and P. Juncar, Opt. Commun. 97, 29-34 (1993)] lasers made use of one of these reference lasers (or the CO2/CO2 system [K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, Appl. Phys. Lett. 22, 192 (1973)]) as an intermediate. The first well-stabilized laser to be measured by a Cs-based frequency chain was the HeNe/CH4 system at 88 THz. [See K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, Appl. Phys. Lett. 22, 192 (1973)]. With interferometric determination of the associated wavelength [R. L. Barger and J. L. Hall, Appl. Phys. Lett. 22, 196-199 (1973)] in terms of the existing wavelength standard based on krypton discharge, the work let to a definitive value for the speed of light, soon confirmed by other laboratories using many different approaches. Redefinition of the unit of length by adopting c=299,792,458 m/s became possible with the extension of the direct frequency measurements to 473 THz (HeNe/I2 633 nm system) 10 years later by a NIST 10-person team, creating a direct connection between the time and length units. More recently, with improved optical frequency standards based on cold atoms (Ca) [H. Schmatz, B. Lipphardt, J. Helmcke, F. Richle, and G. Zinner, Phys. Rev. Lett. 76, 18-21 (1996)] and single trapped ions (Sr+) [J. E. Bernard, A. A. Madej, L. Marmet, B. G. Whitford, K. J. Siemsen, and S. Cundy, Phys. Rev. Lett. 82, 3228-3231 (1999)], these traditional frequency chains have demonstrated measurement uncertainties at the 100 Hz level.
Understandably, these frequency chains are large scale research efforts requiring resources that can be provided by only a few national laboratories. Furthermore, the frequency chain can only cover some discrete frequency marks in the optical spectrum. Difference frequencies of many THz could still remain between a target frequency and a known reference. These three issues have represented major obstacles to making optical frequency metrology a general laboratory tool. Several approaches have been proposed and tested as simple, reliable solutions for bridging large optical frequency gaps. Some popular schemes include: frequency interval bisection [H R. Telle, D. Meschede, and T. W. Hansch, Opt. Lett. 15, 532-534 (1990)], optical-parametric oscillators (OPO) [N. C. Wong, Opt. Lett. 15, 1129-1131 (1990)], optical comb generators [M. Kourogi, K. Nakagawa, and M. Ohtsu, IEEE J. Quantum Electron. 29, 2693-2701 (1993); L. R. Brothers, D. Lee, and N. C. Wong, Opt. Lett. 19, 245-247 (1994)], sum-and-difference generation in the near infrared [D. Van Baak and L. Hollberg, Opt. Lett. 19, 1586-1588 (1994)], frequency division by three [O. Pfister, M. Murtz, J. S. Wells, L. Hollberg, and J. T. Murray, Opt. Lett. 21, 1387-1389 (1996); P. T. Nee and N. C. Wong, Opt. Lett. 23, 46-48 (1998)] and four wave mixing in laser diodes. [See C. Koch and H. R. Telle, J. Opt. Soc. Am. B 13, 1666-1678 (1996)]. All of these techniques rely on the principle of difference-frequency synthesis, in contrast to the frequency harmonic generation method normally used in traditional frequency chains. In the next section we briefly summarize these techniques, their operating principles and applications. Generation of wide bandwidth optical frequency combs has provided the most direct and simple approach among these techniques, and it is the basis for the present invention.
3. Traditional Approaches to Optical Frequency Synthesis. Although the potential for using mode-locked lasers in optical frequency synthesis was recognized early [J. N. Eckstein, A. I. Ferguson, and T. W. Hänsch, Phys. Rev. Lett. 40, 847-850 (1978)], they did not provide the properties necessary for fulfilling this potential until recently. Consequently, an enormous effort has been invested over the last 40 years in “traditional” approaches, which typically involve phase coherently linked single frequency lasers. Traditional approaches to optical frequency measurement can be divided into two sub-categories, one is synthesis by harmonic generation, and the other is difference-frequency synthesis. The former method has a long history of success, at the expense of massive resources and system complexity. The later approach has been the focus of recent research, leading to systems that are more flexible, adaptive and efficient and is the subject of the present invention which involves the use of a wide bandwidth optical frequency comb generator.
a. Phase Coherent Chains (traditional frequency harmonic generation). The traditional frequency measurement takes a synthesis-by-harmonic approach. Harmonics, i.e., integer multiples, of a standard frequency are generated with a nonlinear element and the output signal of a higher-frequency oscillator is phase coherently linked to one of the harmonics. Tracking and counting of the beat note, or the use of a phase-locked loop (PLL), preserves the phase coherence at each stage. Such phase-coherent frequency multiplication process is continued to higher and higher frequencies until the measurement target in the optical spectrum is reached. In the frequency region of microwave to mid-infrared, a harmonic mixer can perform frequency multiplication and frequency mixing/phase comparison all by itself. “Cat's whisker” W—Si point contact microwave diodes, metal-insulator-metal (MIM) diodes and Schottky diodes have been used extensively for this purpose. In the near-infrared to the visible (<1.5 μm), the efficiency of MIM diodes decreases rapidly. Optical nonlinear crystals are better for harmonic generation in these spectral regions. Fast photodiodes perform frequency mixing (non-harmonic) and phase comparison. Such a synthesis chain is a complex system, involving several stages of stabilized transfer lasers, high-accuracy frequency references (in both optical and rf ranges), and nonlinear mixing elements. A important limitation is that each oscillator stage employs different lasing transitions and different laser technologies, so that reliable and cost effective designs are elusive.
1) Local Oscillators and Phase Locked Loops. The most important issue in frequency synthesis is the stability and accuracy associated with such frequency transfer processes. Successful implementation of a synthesis chain requires a set of stable local oscillators at various frequency stages. Maintaining phase coherence across the vast frequency gaps covered by the frequency chain demands that phase errors at each synthesis stage be eliminated or controlled. A more stable local oscillator offers a longer phase coherence time, making frequency/phase comparison more tractable and reducing phase errors accumulated before the servo can decisively express control. Owing to the intrinsic property of the harmonic synthesis process, there are two mechanisms for frequency/phase noise to enter the loop and limit the ultimate performance. The first is additive noise, where a noisy local oscillator compromises the information from a particular phase comparison step. The second, and more fundamental one, is the phase noise associated with the frequency (really phase) multiplication process: the phase angle noise increases as the multiplication factor, hence the phase noise spectral density of the output signal from a frequency multiplier increases as the square of the multiplication factor and so becomes progressively worse as the frequency increases in each stage of the chain. Low phase noise microwave and laser local oscillators are therefore important in all PLL frequency synthesis schemes.
The role of the local oscillator in each stage of the frequency synthesis chain is to take up the phase information from the lower frequency regions and pass it on to the next level, with appropriate noise filtering, and to reestablish a stable amplitude. The process of frequency/phase transfer typically involves phase-locked loops (PLLs). Sometimes, frequency comparison is carried out with a frequency counter measuring the difference in cycle numbers between two periodic signals, within a predetermined time period. As an intrinsic time domain device used to measure zero-crossings, a frequency counter is sensitive to signals—and noise—in a large bandwidth and so can easily accumulate counting errors owing to an insufficient signal-to-noise ratio. Even for a PLL, the possibility of cycle slipping is a serious issue. With a specified signal to noise ratio and control bandwidth, one can estimate the average time between successive cycle slips and thus know the expected frequency counting error. For example, a 100 kHz measurement bandwidth requires a signal-to-noise ratio of 11 dB to achieve a frequency error of 1 Hz (1 cycle slip per 1 s). [See J. L. Hall, M. Taubman, S. A. Diddams, B. Tiemann, J. Ye, L. S. Ma, D. J. Jones, and S. T. Cundiff, in Laser Spectroscopy XIII, edited by R. Blatt, J. Eschner, D. Leibfried and F. Schmidt-Kaler (World Scientific, Singapore, 1999), p. 51-60].
One function of PLLs is to regenerate a weak signal from a noisy background, providing spectral filtering and amplitude stabilization. This function is described as a “tracking filter.” Within the correction bandwidth, the tracking filter frequency output follows the perceived rf input sinewave's frequency. A voltage-controlled-oscillator (VCO) provides the PLL's output constant amplitude, the variable output frequency is guided by the correction error generated from the phase comparison with the weak signal input. A tracking filter, consisting of a VCO under PLL control, is ordinarily essential for producing reliable frequency counting, with the regenerated signal able to support the unambiguous zero-crossing measurement for a frequency counter.
2) Measurements Made With Phase Coherent Chains. As described in the previous section, only a few phase-coherent optical frequency synthesis chains have ever been implemented. Typically, some important infrared standards, such as the 3.39 μm (HeNe/CH4) system and the 10 μm (CO2/OsO4) system are connected to the Cs standard first. Once established, these references are then used to measure higher optical frequencies.
One of the first frequency chains was developed at NBS, connecting the frequency of a methane-stabilized HeNe laser to the Cs standard. [See K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, and G. W. Day, Appl. Phys. Lett. 22, 192 (1973)]. The chain started with a Cs-referenced Klystron oscillator at 10.6 GHz, with its 7th harmonic linked to a second Klystron oscillator at 74.2 GHz. A HCN laser at 0.89 THz was linked to the 12th harmonic of the second Klystron frequency. The 12th harmonic of the HCN laser was connected to a H2O laser, whose frequency was tripled to connect to a CO2 laser at 32.13 THz. A second CO2 laser frequency, at 29.44 THz, was linked to the difference between the 32.13 THz CO2 laser and the third harmonic of the HCN laser. The third harmonic of this second CO2 laser finally reached the HeNe/CH4 frequency at 88.3762 THz. The measured value of HeNe/CH4 frequency was later used in another experiment to determine the frequency of iodine-stabilized HeNe laser at 633 nm, bridging the gap between infrared and visible radiation. [See D. A. Jennings, C. R. Pollock, F. R. Peterson, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, and H. P. Layer, Opt. Lett. 8, 136-138 (1983)].
The important 10 μm spectral region covered by CO2 lasers has been the focus of several different frequency chains. [See C. O. Weiss, G. Kramer, B. Lipphardt, and E. Garcia, IEEE J. Quantum Electron. 24, 1970-1972 (1988); A. Clairon, B. Dahmani, A. Filimon, and J. Rutman, IEEE Trans. Instrum. Meas. 34, 265-268 (1985); B. G. Whitford, App. Phys. B 35, 119-122 (1984)]: It is worth noting that in the Whitford chain [B. G. Whitford, App. Phys. B 35, 119-122 (1984)] a substantial number of difference frequencies (generated between various CO2 lasers) were used to bridge the intermediate frequency gaps, although the general principle of the chain itself is still based on harmonic synthesis. CO2 lasers provided the starting point of most subsequent frequency chains that reached the visible frequency spectrum. [See C. R. Pollock, D. A. Jennings, F. R. Petersen, J. S. Wells, R. E. Drullinger, E. C. Beaty, and K. M. Evenson, Opt. Lett. 8, 133-135 (1983); O. Acef, J. J. Zondy, M. Abed, D. G. Rovera, A. H. Gerard, A. Clairon, P. Laurent, Y. Millerioux, and P. Juncar, Opt. Commun 97, 29-34 (1993). F. Nez, M. D. Plimmer, S. Bourzeix, I. Julien, F. Birabert, R. Felder, O. Acef, J. J. Zondy, P. Laurent, A. Clairon, M. Abed, Y. Millerioux, and P. Juncar, Phys. Rev. Lett. 69, 2326-2329 (1992)]. As noted above, these frequency chains and measurements have led to the accurate knowledge of the speed of light, allowing international redefinition of the “Metre”, and establishment of many absolute frequency/wavelength standards throughout the IR/visible spectrum. More recently, with improved optical frequency standards based on cold atoms (Ca) [H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, Phys. Rev. Lett. 76, 18-21 (1996)] and single trapped ions (Sr+) [J. E. Bernard, A. A. Madej, L. Marmet, B. G. Whitford, K. J. Siemsen, and S. Cundy, Phys. Rev. Lett. 82, 3228-3231 (1999)], these traditional frequency measurement techniques have demonstrated measurement uncertainties at the 100 Hz level, by directly linking the Cs standard to the visible radiation in a single frequency chain.
3) Shortcomings of this Traditional Approach. It is obvious that such harmonic synthesis systems require a significant investment of human and other resources. The systems need constant maintenance and can be afforded only by national laboratories. Perhaps the most unsatisfying aspect of harmonic chains is that they cover only a few discrete frequency marks in the optical spectrum. Therefore the systems work on coincidental overlaps in target frequencies and are difficult to adapt to different tasks. Another limitation is the rapid increase of phase noise (as n2) with the harmonic synthesis order (n).
b. Difference Frequency Synthesis. The difference-frequency generation approach borrows many frequency measurement techniques developed for the harmonic synthesis chains. Perhaps the biggest advantage of difference frequency synthesis over the traditional harmonic generation is that the system can be more flexible and compact, and yet have access to more frequencies. Five recent approaches are disclosed below, with the frequency interval bisection and the optical comb generator being the most significant breakthroughs. The common theme of these techniques is the ability to subdivide a large optical frequency interval into smaller portions with a known relationship to the original frequency gap. The small frequency difference is then measured to yield the value of the original frequency gap.
1) Frequency Interval Bisection. Bisection of frequency intervals is one of the most important concepts in the difference frequency generation. Coherent bisection of optical frequency generates the arithmetic average of two laser frequencies f1 and f2 by phase locking the second harmonic of a third laser at frequency f3 to the sum frequency of f1 and f2. These frequency-interval bisection stages can be cascaded to provide difference-frequency division by 2th. Therefore any target frequency can potentially be reached with a sufficient number of bisection stages. Currently the fastest commercial photodetectors can measure heterodyne beats of some tens of GHz. Thus, six to ten cascaded bisection stages are required to connect a few hundred THz wide frequency interval with a measurable microwave frequency. Therefore the capability of measuring a large beat frequency between two optical signals becomes ever more important, considering the number of bisection stages that can be saved with a direct measurement. A powerful combination is to have an optical comb generator capable of measuring a few THz optical frequency differences as the last stage of the interval bisection chain. It is worth noting that in a difference frequency measurement it is typical for all participating lasers to have their frequencies in a nearby frequency interval, thus simplifying system design. Many optical frequency measurement schemes have been proposed, and some realized, using interval bisection. The most notable achievement so far has been by Hänsch's group at the Max-Planck Institute for Quantum Optics (MPQ) in Garching, where the idea for bisection originated. They used a phase locked chain of five frequency bisection stages to bridge the gap between the hydrogen 1S-2S resonance frequency and the 28th harmonic of the HeNe/CH4 standard at 3.39 μm, leading to the improved measurement of the Rydberg constant and the hydrogen ground state Lamb shift. [See T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, Phys. Rev. Lett. 79, 2646-2649 (1997)]. The chain started with a interval divider between a 486 nm laser (one fourth of the frequency of the hydrogen 1S-2S resonance) and the HeNe/CH4. The rest of the chain successively reduced the gap between this midpoint near 848 nm and the 4th harmonic of HeNe/CH4, a convenient spectral region where similar diode laser systems can be employed, even though slightly different wavelengths are required.
2) Optical Parametric Oscillators. The use of optical parametric oscillators (OPOs) for frequency division relies on parametric down conversion to convert an input optical signal into two coherent subharmonic outputs, the signal and idler. These outputs are tunable and their linewidths are replicas of the input pump except for the quantum noise added during the down conversion process. The OPO output frequencies, or the original pump frequency, can be precisely determined by phase locking the difference frequency between the signal and idler to a known microwave or infrared frequency.
In Wong's original proposal, OPO divider stages configured in parallel or serial were shown to provide the needed multi-step frequency division. [See N. C. Wong, Opt. Lett. 15, 1129-1131 (1990)]. However, no such cascaded systems have been realized so far, owing in part to the difficulty of finding suitable nonlinear crystals for the OPO operation to work in different spectral regions, especially in the infrared. There is progress on the OPO-based optical frequency measurement schemes, most notably optical frequency division by 2 and 3 [S. Slyusarev, T. Ikegami, and S. Ohshima, Opt. Lett. 24, 1856-1858 (1999); A. Douillet, J. J. Zondy, A. Yelisseyev, S. Lobanov, and L. Isaenko, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 47, 1127-1133 (2000)] that allow rapid reduction of a large frequency gap. Along with threshold-free difference frequency generations in nonlinear crystals (discussed next), the OPO system provides direct access to calibrated tunable frequency sources in the IR region (20-200 THz).
3) Nonlinear Crystal Optics. This same principle, i.e., phase-locking between the difference frequency while holding the sum frequency a constant, leads to frequency measurement in the near infrared using nonlinear crystals for the sum-and-difference frequency generation. The sum of two frequencies in the near infrared can be matched to a visible frequency standard while the difference matches to a stable reference in the mid infrared. Another important technique is optical frequency division by 3. This larger frequency ratio could simplify optical frequency chains while providing a convenient connection between visible lasers and infrared standards. An additional stage of mixing is needed to ensure the precise division ratio. [See O. Pfister, M. Murtz, J. S. Wells, L. Hollberg, and J. T. Murray, Opt. Lett. 21, 1387-1389 (1996)].
4) Four Wave Mixing In Laser Diodes. Another approach to difference frequency generation relies on four-wave mixing. The idea [C. Koch and H. R. Telle, J. Opt. Soc. Am. B 13, 1666-1678 (1996)] is to use a laser diode as both a light source and an efficient nonlinear receiver to allow a four-wave mixing process to generate phase-coherent bisection of a frequency interval of a few THz. The setup involved two external cavity diode lasers (ωLD1 and ωLD2), separated by 1-2 THz, that are optically injected into a third diode laser for frequency mixing. When the frequency of the third diode laser (ωLD3) was tuned near the interval center of ωLD1 and ωLD2, the injection locking mechanism became effective to lock ωLD3 on the four-wave mixing product, ωLD1+ωLD2−ωLD3, leading to the interval bisection condition: ωLD3=(ωLd1+ωLD2)/2. The bandwidth of this process is limited by phase matching in the mixing diode, and was found to be only a few THz. [See C. Koch and H. R. Telle, J. Opt. Soc. Am. B 13, 1666-1678 (1996)].
5) Optical Frequency Comb Generators. One of the most promising difference frequency synthesis techniques is the generation of multi-THz optical combs by placing an rf electro-optic modulator (EOM) in a low-loss optical cavity. [See M. Kourogi, K. Nakagawa, and M. Ohtsu, IEEE J. Quantum Electron. 29, 2693-2701 (1993)]. The optical cavity enhances modulation efficiency by resonating with the carrier frequency and all subsequently generated sidebands, leading to a spectral comb of frequency-calibrated lines spanning a few THz. The schematic of such an optical frequency comb generation process is shown in FIGS. 2A and 2B. The single frequency cw laser beam 200, as shown in FIG. 2A, is locked on one of the resonance modes of the EOM cavity, with the free-spectral-range frequency of the loaded cavity being an integer multiple of the EOM modulation frequency. The optical cavity comprises mirrors 208, 210. The optical cavity includes a resonant electro-optic modulator 204 that is driven by a modulator 202 having a modulation frequency fm. The cavity output 206 produces a comb spectrum 212 shown in FIG. 2B with an intensity profile of exp{—|k|π/βF} [M. Kourogi, K. Nakagawa, and M. Ohtsu, IEEE J. Quantum Electron. 29, 2693-2701 (1993)], where k is the order of generated sideband from the original carrier, β is the EOM phase modulation index, and F is the loaded cavity finesse. The uniformity of the comb frequency spacing was carefully verified. [See K. Imai, Y. Zhao, M. Kourogi, B. Widiyatmoko, and M. Ohtsu, Opt. Lett. 24, 214-216 (1999)]. These optical frequency comb generators (OFCG) have produced spectra extending a few tens of THz [K. Imai, M. Kourogi, and M. Ohtsu, IEEE J. Quantum Electron. 34, 54-60 (1998)] nearly 10% of the optical carrier frequency 214. A group at JILA, including the inventors, developed unique OFGCs, one with capability of single comb line selection [J. Ye, L. S. Ma, T. Day, and J. L. Hall, Opt. Lett. 22, 301-303 (1997)] and the other with efficiency enhancement via an integrated OPO/EOM system. [See S. A. Diddams, L. S. Ma, J. Ye, and J. L. Hall, Opt. Lett. 24, 1747-1749 (1999)].
OFCGs had an immediate impact on the field of optical frequency measurement. Kourogi and coworkers [K. Nakagawa, M. deLabachelerie, Y. Awaji, and M. Kourogi, J. Opt. Soc. Am. B 13, 2708-2714 (1996)] produced an optical frequency map (accurate to 10−9) in the telecommunication band near 1.5 μm, using an OFCG that produced a 2-THz wide comb in that wavelength region, connecting various molecular overtone transition bands of C2H2 and HCN. The absolute frequency of the Cs D2 transition at 852 nm was measured against the fourth harmonic of the HeNe/CH4 standard, with an OFCG bridging the remaining frequency gap of 1.78 THz. [See Udem, J. Reichert, T. W. Hansch, and M. Kourogi, Phys. Rev. A 62, 031801—031801—031801-031804 (2000)]. The JILA group used a OFCG to measure the absolute optical frequency of the iodine stabilized Nd:YAG frequency near 532 nm. [See J. L. Hall, L. S. Ma, M. Taubman, B. Tiemann, F. L. Hong, O. Pfister, and J. Ye, IEEE Trans. Instrum. Meas. 48, 583-586 (1999)]. The level scheme for the measurement 310 is shown in FIG. 3. The sum frequency 300 of a Ti:Sapphire laser stabilized on the Rb two photon transition at 778 nm 302 and the frequency doubled Nd:YAG laser 304 was compared against the frequency-doubled output of a diode laser 306 near 632 nm. The 660 GHz frequency gap between the red diode frequency doubled output 306 and the iodine-stabilized HeNe laser 308 at 633 nm was measured using the OFCG. [See J. Ye, L. S. Ma, T. Day, and J. L. Hall, Opt. Lett. 22, 301-303 (1997)].
An OFCG was also used in the measurement of the absolute frequency of a Ne transition (1S5 2P8) at 636.6 nm, relative to the HeNe/I2 standard at 632.99 nm. [See P. Dubé, personal communication 1997; J. Ye, Ph.D Thesis, U. of Colorado (1997)]. The lower level of the transition is a metastable state. Therefore, the resonance can only be observed in a discharged neon cell. The resonance has a natural linewidth of 7.8 MHz. It can be easily broadened (due to unresolved magnetic sublevels) and its center frequency shifted by an external magnetic field. This line is therefore not a high quality reference standard. However, it does have the potential of becoming a low cost and compact frequency reference that offers a frequency calibration on the order of 100 kHz. A red diode laser probing and inexpensive neon lamp form such a system.
The frequency gap between the HeNe/I2 standard and the neon transition is about 468 GHz, which can easily be measured with an OFCG. The HeNe laser, which is the carrier of the comb, is locked to the 127I2 R(127) 11-5 component a13. The neon 1S5 2P8 transition frequency was determined to be 473,143,829.76 (0.10) MHz.
The results obtained using OFCGs made the advantages of larger bandwidth very clear. However the bandwidth achievable by a traditional OFCG is limited by cavity dispersion and modulation efficiency. To achieve even larger bandwidth, mode-locked lasers were introduced, thus triggering a true revolution in optical frequency measurement. Mode-locked lasers are employed in accordance with the present invention.